The UN cultural agency on Tuesday adopted an Arab-sponsored resolution condemning Israel's actions at a flashpoint holy site in east Jerusalem, deepening anger in the Jewish state.
On Friday, Renzi strongly criticised the resolution, saying that Rome --which had abstained in the vote -- would now oppose it.
"It is incomprehensible and unacceptable, a mistake. I specifically asked diplomats involved in such cases yesterday (Thursday) not to continue like this -- we cannot deny reality," Renzi told an Italian radio station.
"To say that the Jewish people has no connection to Jerusalem is like saying that the sun creates darkness."
"If we have to break European ranks on this issue, then so be it," Renzi said.
In a statement, Netanyahu's office said the two premiers spoke on Saturday and that the Israeli prime minister told Renzi that "even the theatre of the absurd has limits".
The statement said Renzi told Netanyahu he "would work to influence the positions of other European countries" in similar votes in the future.
Tuesday's UNESCO resolution on "occupied Palestine" was endorsed by the agency's executive board at its headquarters in Paris, after being approved at the committee stage last week.
Israel considers all of Jerusalem as its undivided capital, but the Palestinians want the eastern sector as capital of their future state.
Israel is furious that the resolution refers to the Old City site in Jerusalem by its Muslim name, Al-Aqsa or Al-Haram al-Sharif.
It is considered holy by Muslims, Christians and Jews. Jews refer to it as the Temple Mount and it is considered the holiest site in Judaism.